Agreed, but unless you are in a "clean" room like the computer chip manufacturers, a lot of other things in the room can be the source of mildew. Lots of stuff, curtains, plywood, carpet, ceiling tiles, paper, and air itself can do this. You can get it all.
I'm not sure I would worry too much about sanitizing the weights as much as the surfaces that would come in direct contact with the cheese itself. That is; spoons, pans, trays, tables, whisks, followers knives, strainers, followers, cheese clothes, moulds etc.
But that is just me.